Answered: it. Wrapped around the smaller disk is…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter3: Force And Motion

Section3.3: Newton’s Second Law Of Motion

Problem 1PQ: How are force and motion related?

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A large solid disk with radius r_b= 1.1m has a second, smaller solid disk with radius r_s= 0.32m and mass m_s= 3.5kg attached to it. Wrapped around the smaller disk is an ideal string with a hanging mass m_h= 2.3kg attached to it. The hanging mass starts out a distance y_i= 5.2m above the ground as shown in Figure 1, and falls towards the ground with constant speed.

a) What is the torque about the center of the pulleys? Remember torque is a vector.

b) What should the mass of the larger pulley be such that the system of pulleys has an angular acceleration of α = 1.2rad/s ?

c) How long will it take the hanging mass to hit the ground?

Tb
Ts
mh
Yi
Figure 1: Pulley system with hanging mass attached.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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